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The structure of binary coproducts in the category of frames is analyzed, and the results are then applied widely in the study of compactness, local compactness (continuous frames), separatedness, pushouts and closed frame homomorphisms.

On bisemilattices. I

J. Dudek (1982)

Colloquium Mathematicae

On blockers in bounded posets.

Matveev, Andrey O. (2001)

International Journal of Mathematics and Mathematical Sciences

On Boolean modus ponens.

Sergiu Rudeanu (1998)

Mathware and Soft Computing

An abstract form of modus ponens in a Boolean algebra was suggested in [1]. In this paper we use the general theory of Boolean equations (see e.g. [2]) to obtain a further generalization. For a similar research on Boolean deduction theorems see [3].

On Boolean partial differential equations

Sergiu Rudeanu (2001)

Kragujevac Journal of Mathematics

On bounding congruences in some algebras having the lattice structure

J. Płonka (1982)

Banach Center Publications

On BPI Restricted to Boolean Algebras of Size Continuum

Eric Hall, Kyriakos Keremedis (2013)

Bulletin of the Polish Academy of Sciences. Mathematics

(i) The statement P(ω) = “every partition of ℝ has size ≤ |ℝ|” is equivalent to the proposition R(ω) = “for every subspace Y of the Tychonoff product $2^{(ω)}$ the restriction |Y = Y ∩ B: B ∈ of the standard clopen base of $2^{(ω)}$ to Y has size ≤ |(ω)|”. (ii) In ZF, P(ω) does not imply “every partition of (ω) has a choice set”. (iii) Under P(ω) the following two statements are equivalent: (a) For every Boolean algebra of size ≤ |ℝ| every filter can be extended to an ultrafilter. (b) Every Boolean algebra of...

On branchwise implicative BCI-algebras.

Chaudhry, Muhammad Anwar (2002)

International Journal of Mathematics and Mathematical Sciences

On Butler $B (2)$ -groups decomposing over two base elements

Clorinda de Vivo, Claudia Metelli (2009)

Commentationes Mathematicae Universitatis Carolinae

A $B (2)$ -group is a sum of a finite number of torsionfree Abelian groups of rank $1$ , subject to two independent linear relations. We complete here the study of direct decompositions over two base elements, determining the cases where the relations play an essential role.

On Carathéodory vector lattices

Ján Jakubík (2003)

Mathematica Slovaca

On Carathéodory's and Krein-Milman's theorems in fully ordered groups

Siegfried Helbig (1988)

Commentationes Mathematicae Universitatis Carolinae

On CCC boolean algebras and partial orders

András Hajnal, István Juhász, Zoltán Szentmiklóssy (1997)

Commentationes Mathematicae Universitatis Carolinae

We partially strengthen a result of Shelah from [Sh] by proving that if $κ = κ^{ω}$ and $P$ is a CCC partial order with e.g. $| P | \leq κ^{+ ω}$ (the $ω^{th}$ successor of $κ$ ) and $| P | \leq 2^{κ}$ then $P$ is $κ$ -linked.

On centers and state spaces of logics

Pták, Pavel (1984)

Proceedings of the 11th Winter School on Abstract Analysis

On central atoms of Archimedean atomic lattice effect algebras

Martin Kalina (2010)

Kybernetika

If element $z$ of a lattice effect algebra $(E, \oplus, 0, 1)$ is central, then the interval $[0, z]$ is a lattice effect algebra with the new top element $z$ and with inherited partial binary operation $\oplus$ . It is a known fact that if the set $C (E)$ of central elements of $E$ is an atomic Boolean algebra and the supremum of all atoms of $C (E)$ in $E$ equals to the top element of $E$ , then $E$ is isomorphic to a direct product of irreducible effect algebras ([16]). In [10] Paseka and Riečanová published as open problem whether $C (E)$ is a bifull sublattice...

On central relations of complete lattices

Dietmar Schweigert, Magdalena Szymańska (1987)

Czechoslovak Mathematical Journal

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